The semiflexible fully-packed loop model and interacting rhombus tilings

Abstract

Motivated by a recent adsorption experiment [M.O. Blunt et al., Science 322, 1077 (2008)], we study tilings of the plane with three different types of rhombi. An interaction disfavors pairs of adjacent rhombi of the same type. This is shown to be a special case of a model of fully-packed loops with interactions between monomers at distance two along a loop. We solve the latter model using Coulomb gas techniques and show that its critical exponents vary continuously with the interaction strenght. At low temperature it undergoes a Kosterlitz-Thouless transition to an ordered phase, which is predicted from numerics to occur at a temperature T \sim 110K in the experiments.

4 pages, 4 figures, v2: corrected typo, v3: minor modifications, published version

References in corpus (5)

• Geometric Frustration in Buckled Colloidal Monolayers
• Interacting classical dimers on the square lattice
• Classical dimers with aligning interactions on the square lattice
• Continuous melting of compact polymers
• Conformal field theory of the Flory model of polymer melting

Cited by in corpus (9)

• Broken symmetry and the variation of critical properties in the phase behaviour of supramolecular rhombus tilings
• Random and ordered phases of off-lattice rhombus tiles
• Geometric Frustration of Colloidal Dimers on a Honeycomb Magnetic Lattice
• Classical dimer model with anisotropic interactions on the square lattice
• Entropically-stabilised growth of a two-dimensional random tiling
• Monomer-Dimer Mixture on a Honeycomb Lattice
• Kosterlitz-Thouless transitions and phase diagrams of the interacting monomer-dimer model on a checkerboard lattice
• Color-dependent interactions in the three coloring model
• Classical fully-packed loop model with attractive interactions on the square lattice